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Abstract:
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In the setting of competing risks, it is often of interest to estimate the marginal survival function, defined as the probability of a specific event occurring if all other causes of failure were suppressed. For example, survival of patients on the liver transplant waiting list is of interest in the absence of transplantation. However, the marginal survival functions are nonidentifiable without making further assumptions, the majority of which are untestable. One exception is the random signs censoring (RSC) assumption which assumes the main event time distribution is independent of the indicator that the main event preceded the competing event. Thus far, few methods have been developed to formally test this assumption, and none have considered testing the more relaxed conditional random signs censoring (CRSC) assumption, which allows for RSC to be met after conditioning on covariates. In this paper, we develop a nonparametric test for CRSC conditional on a categorical covariate. We study analytically the properties of the proposed test statistic, evaluate its finite-sample properties using Monte Carlo simulations, and illustrate its use via an application to real data.
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